(-4x+10/x-4)=1

Solution for (-4x+10/x-4)=1 equation:

(-4x+10/x-4)=1

We move all terms to the left:

(-4x+10/x-4)-(1)=0


Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

-4x+10/x-4-1=0

We multiply all the terms by the denominator


-4x*x-4*x-1*x+10=0

We add all the numbers together, and all the variables

-5x-4x*x+10=0

Wy multiply elements

-4x^2-5x+10=0

a = -4; b = -5; c = +10;
Δ = b2-4ac
Δ = -52-4·(-4)·10
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{185}}{2*-4}=\frac{5-\sqrt{185}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{185}}{2*-4}=\frac{5+\sqrt{185}}{-8}
$